Deck 9: The Time Value of Money

Question 1

As the interest rate increases, the PV_IF for the present value of $1 increases.

Answer 1

False

Question 2

The future value of an annuity assumes that the payments are received at the end of the year and that the last payment does not compound.

Answer 2

True

Question 3

The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year.

Answer 3

True

Question 4

The amount of annual payments necessary to accumulate a desired total can be found by reference to the present value of an annuity table.

Question 5

The amount of annual payments necessary to repay a mortgage loan can be found by reference to the present value of an annuity table.

Question 6

The interest factor for the future value of an annuity is simply the sum of the interest factors for the future value using the same number of periods.

Question 7

The time value of money is not a useful concept in determining the value of a bond or in capital investment decisions.

Question 8

The interest factor for a future value (FV_IF) is equal to (1 + i)ⁿ.

Question 9

An amount of money to be received in the future is worth less today than the stated amount.

Question 10

In determining the PV_IF for the present value of $1, one could use the reciprocal of the FV_IF for the future value of $1 at the same rate and time period.

Question 11

If a single amount were put on deposit at a given interest rate and allowed to grow, its future value could be determined by reference to the Compound Sum of $1 table.

Question 12

To determine the current worth of 4 annual payments of $1,000 at 4%, one would refer to a table for the present value of $1.

Question 13

Inflation is the most important reason that a dollar today is worth more than a dollar in the future.

Question 14

If an individual's cost of capital were 10%, he or she would prefer to receive $107 at the end of one year rather than $100 right now.

Question 15

An annuity is a series of consecutive payments of equal amount.

Question 16

The formula FV = PV(1 + n)ⁱ will determine the present value of $1.

Question 17

In evaluating capital investment projects, current outlays must be judged against the current value of future benefits.

Question 18

In paying off a mortgage loan, the amount of the periodic payment that goes toward the reduction of principal increases over the life of the mortgage.

Question 19

In determining the future value of an annuity, the final payment is not compounded at all.

Question 20

The annualized return on an investment can be determined by reference to a table for the present value of $1.

Question 21

If you were to put $1,000 in the bank at 6% interest each year for the next 10 years, which table would you use to find the ending balance in your account?

A) present value of $1
B) future value of $1
C) present value of an annuity of $1
D) compound sum of an annuity of $1

Question 22

The FV_IFA for the future value of an annuity is 4.5 at 10% for 4 years. If we wish to accumulate $8,000 by the end of 4 years, how much should the annual payments be?

A) $2,500
B) $2,000
C) $1,778
D) $2,200

Question 23

The present value of a positive future value may become negative as discount rates become higher and higher.

Question 24

As the interest rate increases, the present value of an amount to be received at the end of a fixed period

A) increases.
B) decreases.
C) remains the same.
D) not enough information to tell

Question 25

Pension fund retirement accounts use the present value of an annuity to calculate the ending value upon retirement.

Question 26

The interest factor for the present value of a single sum is equal to (1+i)/i.

Question 27

An annuity may be defined as

A) a payment at a fixed interest rate.
B) a series of payments of unequal amount.
C) a series of yearly payments.
D) a series of consecutive payments of equal amounts.

Question 28

Under what conditions must a distinction be made between money to be received today and money to be received in the future?

A) a period of recession
B) when idle money can earn a positive return
C) when there is no risk of nonpayment in the future
D) when current interest rates are different from expected future rates

Question 29

Cash flow decisions that ignore the time value of money will probably not be as accurate as those decisions that do rely on the time value of money.

Question 30

The future value is the same concept as the way money grows in a bank account.

Question 31

The time value of money concept becomes less critical as the prime rate increases.

Question 32

Using semiannual compounding rather than annual compounding will increase the future value of an annuity.

Question 33

When the inflation rate is zero, the present value of $1 is identical to the future value of $1.

Question 34

The interest factor for the present value of a single amount is the inverse of the future value interest factor.

Question 35

A dollar today is worth more than a dollar to be received in the future because

A) risk of nonpayment in the future.
B) the dollar can be invested today and earn interest.
C) inflation will reduce purchasing power of a future dollar.
D) none of the other choices-a dollar today is not worth more than a dollar to be received in the future

Question 36

A home buyer signed a 20-year, 8% mortgage for $72,500. How much should the annual loan payments be? (Assume annual compounding.)

A) $5,560
B) $7,384
C) $8,074
D) $13,900

Question 37

The farther into the future any given amount is received, the larger its present value.

Question 38

You are to receive $12,000 at the end of 5 years. The available yield on investments is 6%. Which table would you use to determine the value of that sum today?

A) present value of an annuity of $1
B) future value of an annuity
C) present value of $1
D) compound sum of $1

Question 39

Higher interest rates (discount rates) reduce the present value of amounts to be received in the future.

Question 40

As the time period until receipt increases, the present value of an amount at a fixed interest rate

A) decreases.
B) remains the same.
C) increases.
D) not enough information to tell

Question 41

Mr. Darden is selling his house for $165,000. He bought it for $55,000 nine years ago. What is the annual return on his investment?

A) 13%
B) 22%
C) 33%
D) 200%

Question 42

To find the yield on investments that require the payment of a single amount initially, and which then return a single amount some time in the future, the correct table to use is

A) the future value of $1.
B) the compound sum of $1.
C) present value of an annuity of $1.
D) all the answers are correct

Question 43

Increasing the number of periods will increase all of the following except

A) the present value of an annuity.
B) the present value of $1.
C) the future value of $1.
D) the future value of an annuity.

Question 44

Ambrin Corp. expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20 year cash flow? Use an 11% discount rate.

A) $19,038
B) $27,872
C) $32,391
D) $15,927

Question 45

Mr. Fish wants to build a house in 10 years. He estimates that the total cost will be $170,000. If he can put aside $10,000 at the end of each year, what rate of return must he earn in order to have the amount needed?

A) between 11% and 12%
B) between 8% and 9%
C) 17%
D) none of the other answers are correct

Question 46

A 20-year mortgage with monthly payments has a principal outstanding of $125,000. Interest is at 8% compounded semi-annually. What are the monthly payments?

A) $ 833.33
B) $1,035.45
C) $1,045.55
D) $1,354.16

Question 47

Mr. Nailor invests $5,000 in a certificate of deposit at his local bank. He receives annual interest of 8% for 7 years. How much interest will his investment earn during this time period?

A) $2,915
B) $3,569
C) $6,254
D) $8,570

Question 48

Mr. Blochirt is creating a university investment fund for his daughter. He will put in $850 per year at the end of each year for the next 15 years and expects to earn an 8% annual rate of return. How much money will his daughter have when she starts university?

A) $11,250
B) $12,263
C) $24,003
D) $23,079

Question 49

Dr. J. wants to buy an IBM personal computer which will cost $2,788 four years from today. He would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. He can earn a 7% annual return. How much should he set aside?

A) $697.00
B) $627.94
C) $823.15
D) $531.81

Question 50

Lou Lewis borrows $10,000 to be repaid over 10 years with equal annual payments at 9 percent. Repayment of principal in the first year is

A) $1,558.20.
B) $1,000.00.
C) $ 900.00.
D) $ 658.20.

Question 51

The concept of time value of money is important to financial decision making because

A) it emphasizes earning a return on invested capital.
B) it recognizes that earning a return makes $1 worth more today than $1 received in the future.
C) it can be applied to future cash flows in order to compare different streams of income.
D) all of the other answers are correct

Question 52

In determining the compound sum of a single amount, one measures

A) the future value of periodic payments at a given interest rate.
B) the present value of an amount discounted at a given interest rate.
C) the future value of an amount allowed to grow at a given interest rate.
D) the present value of periodic payments at a given interest rate.

Question 53

Football player Walter Johnson signs a contract calling for payments of $2,500,000 per year, to begin 10 years from now. To find the present value of this contract, which table or tables should you use?

A) the future value of $1
B) the future value of an annuity of $1 and the future value of $1
C) the present value of an annuity of $1 and the present value of $1
D) the present value of an annuity of $1

Question 54

After 20 years, 100 shares of stock originally purchased for $1,000 was sold for $5,000. What was the annual yield on the investment? Choose the closest answer.

A) 19.00%
B) 5.00%
C) 12.70%
D) 8.38%

Question 55

The shorter the length of time between a present value and its corresponding future value,

A) the lower the present value, relative to the future value.
B) the higher the present value, relative to the future value.
C) the higher the interest rate used in the present-valuation.
D) none of the other answers are correct

Question 56

Joe Nautilus has $120,000 and wants to retire. What return must his money earn so he may receive annual benefits of $20,000 for the next 14 years?

A) 12%
B) between 12% and 13%
C) 14%
D) greater than 15%

Question 57

A retirement plan guarantees to pay to you or your estate a fixed amount for 20 years. At the time of retirement you will have $73,425 to your credit in the plan. The plan anticipates earning 9% interest. How much will your annual benefits be?

A) $1,435
B) $3,671
C) $6,608
D) $8,043

Question 58

Babe Ruth Jr. has agreed to play for the Toronto Blue Jays for $9 million per year for the next 10 years. What table would you use to calculate the value of this contract in today's dollars?

A) present value of an annuity
B) present value of a single amount
C) future value of an annuity
D) none of the other answers are correct

Question 59

John Doeber borrowed $125,000 to buy a house. His loan cost was 11% and he promised to repay the loan over 15 years (amortization). How much are the monthly payments with semiannual compounding?

A) $1,146
B) $1,380
C) $1,421
D) $1,402

Question 60

The higher the discount rate used in determining the future value of a $1 annuity,

A) the greater the future value at the end of a period.
B) the smaller the future value at the end of a period.
C) the greater the present value at the beginning of a period.
D) none of the other answers are correct: the interest has no effect on the future value of an annuity.

Question 61

Sara Shouppe has invested $100,000 in an account at her local bank. The bank will pay her a constant amount each year for 6 years, starting one year from today, and the account's balance will be 0 at the end of the sixth year. If the bank has promised Ms. Shouppe a 10% return, how much will they have to pay her each year?

Question 62

Gary Kiraly wants to buy a new Italian sports car in three years. The vehicle is expected to cost $80,000 at that time. If Gary should be so lucky as to find an investment yielding 12% over that three-year period, how much would he have to invest now in order to accumulate $80,000 at the end of the three years?

Question 63

Sharon Smith will receive $1,000,000 in 50 years. The discount rate is 14%. As an alternative she can receive $2,000 today. Which should she choose?

A) the $1,000,000 in 50 years.
B) the $2,000 today.
C) she should be indifferent.
D) it depends on the inflation rate.

Question 64

In January, 19925 Harold Black bought 100 shares of Country homes for $37.50 per share. He sold them in January, 2005 for a total of $9,727.50. Calculate Harold's annual rate of return.

Question 65

Marcia Stubern is planning for her golden years. She will retire in 20 years, at which time she plans to begin withdrawing $60,000 annually. She is expected to live for 20 years following her retirement. Her financial advisor thinks she can earn 9% annually. How much does she need to invest each year to prepare for her financial needs after her retirement?

Question 66

If we wish to accumulate $8,000 by the end of 4 years, how much should the annual payments be if we receive an interest rate of 10% on our investments? The first payment is made at the end of each year.

A) $2200
B) $2,000
C) $1,723.77
D) $2,200

Question 67

As the time period until receipt decreases, the present value of an amount at a fixed interest rate

A) decreases.
B) remains the same.
C) increases.
D) not enough information to tell

Question 68

Samuel Johnson invested in gold Maple Leaf coins 10 years ago, paying $185 for each one-ounce gold coin. He could sell each coin for $734 today. What was his annual rate of return for this investment?

Question 69

Mr. Sullivan is borrowing $2 million to expand his business. The loan will be for 10 years at 12% on the declining balance, and will be repaid in equal quarterly instalments. What will the quarterly payments be? At the end of the first year, how much interest will Mr. Sullivan have paid? By how much will he have reduced the principal?

Question 70

Pedro Gonzalez will invest $5,000 at the beginning of each year for the next 9 years. The current yield is 8%. What is the future value?

A) $45,000.
B) $62,438.
C) $67,433.
D) $60,105.

Question 71

You have an opportunity to buy a $1,000 bond, which matures in 10 years. The bond pays $30 every six months. The current market interest rate is 8%. What is the most you would be willing to pay for this bond?

Question 72

You will deposit $2,000 today. It will grow for 6 years at 10% interest compounded semiannually. You will then withdraw the funds annually over the next 4 years. The annual interest rate is 8%. Your annual withdrawal will be

A) $2,340.
B) $4,332.
C) $797.
D) $1,084.

Question 73

The future value of a $1,000 investment today at 8% annual interest compounded semiannually for 5 years is

A) $1,469.
B) $1,480.
C) $1,520.
D) $1,555.

Question 74

Carol Thomas will pay out $6,000 at the end of the year 2, $8,000 at the end of year 3, and receive $10,000 at the end of year 4. With an interest rate of 13%, how much money does she need to have on hand today to meet her obligations?

A) $4,110.
B) $10,243.
C) $14,000.
D) $4,000.

Question 75

The Swell Computer Company has developed a new line of desktop computers. It is estimated that the cash returns generated by the new product line will be $800,000 per year for the next five years, and then $500,000 per year for 3 years after that (the cash returns occur at the end of each year). At a 9% interest rate, what is the present value of these cash returns?

Question 76

As the interest rate decreases, the present value of an amount to be received at the end of a fixed period

A) increases.
B) decreases.
C) remains the same.
D) not enough information to tell

Question 77

As the discount rate becomes higher and higher, the present value of inflows approaches

A) 0.
B) minus infinity.
C) plus infinity.
D) need more information

Question 78

If you were to put $5,000 in the bank at 4% interest each year for the next 8 years, which table would you use to find the ending balance in your account?

A) present value of $1
B) future value of $1
C) present value of an annuity of $1
D) compound sum of an annuity of $1

Question 79

Janice Hardin sets aside $5,000 each year for 10 years. She then withdraws the funds on an equal annual basis for the next 10 years. The two tables she should use in the correct order are:

A) present value of an annuity of $1; future value of an annuity of $1.
B) future value of an annuity of $1; present value of an annuity of $1.
C) future value of an annuity of $1; present value of $1.
D) future value of an annuity of $1; future value of $1.

Question 80

Mike Carlson will receive $10,000 a year from the end of the third year to the end of the 12^th year (10 payments). The discount rate is 10%. The present value today of this deferred annuity is

A) $61,446.
B) $55,860.
C) $46,165.
D) $50,782.